Self- tuning regulators and controllers have proven to be a useful industrial control device. The self- tuning theory upon which these devices are based comprises the two aspects: controller design and system identification. In this first paper the emphasis is on the design, or more correctly, the synthesis, of the controller. In particular, classes of optimal controllers each dependent on a different cost function are discussed. The two most popular controllers- the minimum variance and the generalised minimum variance control laws - are derived in this first part.
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